TITLE: Is the choice of textbook really that important?
QUESTION [12 upvotes]: I am an undergraduate student in mathematics and I met a student from another university recently. He told me that it is useless to study those textbooks that are rather simple compared to others. (For example, Bartle's Analysis compared to Rudin's Analysis.) I feel extremely sad for what he said since I literally studied almost all subjects of pure mathematics for which he mentioned as simple textbooks. I studied Functional Analysis from Kreysig, I studied Real Analysis from Wilcox, I studied Linear Algebra from Anton and Modern Algebra from Fraleigh, etc...
Is it really that bad if I didn't study those advanced texts like Rudin's, Artin, Herstein, etc? Is the choice of books matter that much?

REPLY [3 votes]: Choice of the textbook might matter to some extent, but there are several angles to it.

For learning the material, find whichever book suits you the best. It might be useful to go to a library and surf through some books, or ask for some book recommendations from stack-exchange. It might also be fine to go for a combination of different textbooks. For this step, the priority is to see that new concepts make sense to you.
Now that you have learnt some new ideas, what's next? Find exercises to solve. Again, you can find them from a combination of multiple books. Furthermore, if you can successfully solve problems from the "unfriendly" books as well, then your understanding is just as good.
Try skimming through the unfriendly books anyway, at the end. See if there are things that are things explained in a differrent light. Also, one of the skills that'd be necessary for a mathematician would be to understand new things from hard-to-read sources. I suspect that as a professional mathematician, you would encounter papers which are hard to understand for various reasons. This means, it is useful to be able to understand material which is written in slightly dry ways.